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Adding relations to a poset

I am trying to write a program that proves that some set of inequalities is not compatible. I am trying to do this with Sage's Poset class. My idea is to create a basic poset, then gradually add relations, then finally check the number of linear extensions.

The only problem is: I didn't find a way to add relations to an existing Poset. How do I do this in Sage?

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Adding relations to a poset

I am trying to write a program that proves that some set of inequalities is not compatible. I am trying to do this with Sage's Poset class. My idea is to create a basic poset, then gradually add relations, then finally check the number of linear extensions.

The only problem is: I didn't find a way to add relations to an existing Poset. How do I do this in Sage?